The 45-year-old, sacked as Italy coach in June when the world champions went out of Euro 2008 in the quarter-finals, has replaced the sacked Edy Reja at the Serie A side.
The Naples club had been pushing for a Champions League or UEFA Cup spot but nine league games without a win have left them languishing in 11th spot.
"The team is not going through an easy moment, it doesn't make sense to talk about Europe," Donadoni told a news conference on Wednesday.
"First I have to understand what players I have at my disposal. I will talk with Reja and with the players, then I will start work. I have ideas but first I must confront my new reality."
Donadoni's Italy side, which lost on penalties to winners Spain in June, was criticised for its tactical naivety and lack of flair.
The former AC Milan midfielder became national coach in 2006 despite a relatively short stint as a domestic manager where he succeeded in helping Livorno reach the UEFA Cup.
Napoli, backed by a huge fanbase and the money of film producer Aurelio De Laurentiis, are in their second season back in the top flight and have two of Serie A's hottest prospects -- Slovakia's Marek Hamsik and Argentine forward Ezequiel Lavezzi.
The club from Italy's third biggest city won their only two scudettos in 1987 and 1990 thanks to Diego Maradona.
Reja masterminded Napoli's rise from the third tier to Serie A in five years but Sunday's 2-0 home defeat by Lazio was the final straw.
"I told Reja that the dressing room was no longer with him and that a change was needed for the team to return to how it was before," De Laurentiis said.
"I had already thought of Donadoni... and spoken to him in previous times of crisis."
